# How to calculate the distance between two points in projective plane

I have two homogeneous coordinates and I am trying to preserve the distance between two coordinates after various affine trasnformations. Should I calculate the angle between two points ? If so what is the formula to calculate the angle between two points or is there a distance formula other than the general euclidean plane? I found that euclidean distance formula will not preserve the distances

what is the distance formula between two homogeneous coordinates

• There's no such thing as distance in the projective plane -- it becomes projective partly from ignoring the concept of distance. – Henning Makholm Jan 23 '17 at 21:01
• @HenningMakholm So should I calculate the angle between the coordinates ? – vinaykva Jan 23 '17 at 21:03
• That depends entirely on what you want to achieve. (Note that this angle, if I understand correctly what you mean, is not a projective invariant). – Henning Makholm Jan 23 '17 at 21:04
• @HenningMakholm Assume I have a camera and I am moving towards the camera and away from the camera – vinaykva Jan 23 '17 at 21:06
• What do you mean by “I am trying to preserve the distance […] after various affine transformations”? Is it that you have the affine trafos and want to show that they preserve distance? Or check whether they do preserve distance? Or is it that you want to append one more transformation in order to make distances as they were? If so, what kind of transformation? Or is it that you want to tune some parameters to ensure that distances are preserved? Do you want to preserve orientation as well, or may orientation be reversed? – MvG Jan 24 '17 at 12:03